Continuous maps of the interval with finite nonwandering set

Block, Louis

doi:10.1090/S0002-9947-1978-0474240-2

Continuous maps of the interval with finite nonwandering set
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Trans. Amer. Math. Soc. 240 (1978), 221-230 Request permission

Abstract:

Let f be a continuous map of a closed interval into itself, and let $\Omega (f)$ denote the nonwandering set of f. It is shown that if $\Omega (f)$ is finite, then $\Omega (f)$ is the set of periodic points of f. Also, an example is given of a continuous map g, of a compact, connected, metrizable, one-dimensional space, for which $\Omega (g)$ consists of exactly two points, one of which is not periodic.

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